A model Hamiltonian of the BCS type for a Bose gas

A study is made of a model Hamiltonian of BCS type for a Bose gas and it is given a rigorous mathematieal meaning tn the ease of an infinite volume. The grand partition function is calculated and an equation of state is found, it is shown that in the ease of an infinite volume the chain of equations for the Green's functions has two solutions: free Green's funetions and Green's functions of the approximating Hamittonian.